Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
If you think that mathematical proof is really clearcut and universal then you should read this article.
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Keep constructing triangles in the incircle of the previous triangle. What happens?
Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Which of these roads will satisfy a Munchkin builder?
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
Can you rearrange the cards to make a series of correct mathematical statements?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
When is it impossible to make number sandwiches?
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
This is the second article on right-angled triangles whose edge lengths are whole numbers.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
An article which gives an account of some properties of magic squares.